Benchmark: We select 31 benchmarks of different sizes and various applications.
For the SC backend, we select VQE UCCSD ansatzes [1]} of six sizes, and the QAOA programs [2]} for graph max-cut on regular (REG) graphs of degrees 4, 8, 12, and random (Rand) graphs of edge probability 0.1, 0.3, 0.5, as well as traveling salesman problem (TSP) of different sizes.
These benchmarks are generated by Qiskit [3]}.
For the FT backend, we first generate the Hamiltonians of five molecules using PySCF [4]} (\(\rm N_2\) , \(\rm H_2S\) , \(\rm MgO\) , \(\rm CO_2\) , \(\rm NaCl\) ).
We also prepare the Hamiltonians of three Ising models and three Heisenberg models, both of which are widely used in condensed matter physics, of different dimensions.
We finally generate random Hamiltonians (Rand) of various sizes (30 to 80 qubits) for a more comprehensive evaluation.
For a Hamiltonian of \(n\)  qubits, we prepare \(5n^2\)  Pauli strings. In each Pauli string, we first randomly select one integer \(m\)  between 1 and \(n\) . Then we randomly select \(m\)  qubits and assign random Pauli operators to them.
The rest \(n-m\)  qubits will be assigned with the identity.
Table REF  shows the details of these benchmarks.
Note that `Pauli #' represents the number of Pauli strings. We include the \(\rm CNOT\)  and single-qubit gate counts when naively converting these benchmarks into gates without any optimization/transformations,
and neglecting mapping overhead.
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